Compressible structure secured to an upper of an article of footwear

ABSTRACT

An article of footwear has an upper and a compressible structure secured to the upper. The compressible structure can include one or more materials with physical properties that singly or in vertical aggregate, generally conform to those of a spring, following Hooke&#39;s Law, F=−kx, whereby the ratio of k/kideal approaches a value of 1.0, wherein the ideal k value is defined as kideal=Fimpulsexs-max, for a compressible structure region located adjacent to the corresponding region of the foot that generates the force impulse.

The presently disclosed technology is directed to cushioning and energy return systems for athletic shoes that increase athletic performance by engineering the rebound characteristics of the sole components to optimize the conversion of kinetic energy from the foot of the wearer into potential energy stored within the sole components and subsequently converting that potential energy back into useful kinetic energy. Given a vertical force magnitude from the foot and a specified proportionality limit for the sole, there is a unique value for the spring constant, k (N/m), which will yield the maximum energy return. The system is said to be tuned when the spring constant yields the maximum useful spring potential energy for a given force and the maximum spring compression.

The presently disclosed technology vertical ground reaction force data for discrete anatomical regions under the foot at a range of running speeds. Energy return can be maximized for different running speeds, by adjusting the spring constant according to the force from a foot region associated with a particular running speed. The presently disclosed technology allows for either the specification of the physical properties of sole components to be tuned to a running speed, or for the identification of running speeds that will experience the greatest energy return given the physical properties of the sole.

BACKGROUND

Conventional articles of athletic footwear include two primary elements, an upper and a sole structure. The upper is generally formed from a plurality of elements (e.g., textiles, foam, leather, synthetic leather) that are stitched or adhesively bonded together to form an interior void for securely and comfortably receiving a foot. The sole structure incorporates multiple layers that are conventionally referred to as a sockliner, a midsole, and an outsole. The sockliner is a thin, compressible member located within the void of the upper and adjacent to a plantar (i.e., lower) surface of the foot to enhance comfort through the distribution of pressure over the plantar surface of the foot. The midsole is the compressible layer secured to the upper and forms a structure that attenuates ground reaction forces on the foot by doing work to convert kinetic energy of the foot into potential energy (i.e., imparts cushioning), and can do work to turn stored potential energy back into kinetic energy (i.e. energy return) during walking, running, or other ambulatory activities. The outsole forms a ground-contacting element of the footwear and is usually fashioned from a durable and wear-resistant material that includes texturing to impart traction. The outsole may constitute part of the compressible layer, may be non-compressible, and may cover a portion of the ground contacting surface.

The primary material forming many conventional compression layers is a polymer foam, such as polyurethane, olefin, or ethylvinylacetate. In some articles of footwear, the compression layer may also incorporate structures in the form of molded plastics or metal alloys in the form of conical, cylindrical, or leaf springs, or fluid/gas-filled chambers, which modify the cushioning and energy return properties of the compression layer. Many configurations of polymer material and incorporated structures purport to deliver varying degrees of cushioning and energy return.

Articles of footwear intended for sports activities such as running have compressible layers designed to respond to vertical compressive forces. Such compressible layers may also be designed to react to lateral and shear forces, and can be designed for either or both purposes simultaneously. Compressible layers acting in the vertical plane and behaving much like springs, can exhibit both cushioning and energy return properties. Together, the compression phase and the expansion phase are known as rebound.

Compressible layers with rebound properties can be modeled mathematically according to Hooke's Law [1] and Newtons 2^(nd) Law [2]. Elastic 3-dimensional materials have been shown to exhibit spring-like qualities and to be accurately modeled mathematically with simple substitutions to translate from a 1-dimensional spring to a 3-dimensional solid. For clarity of explanation and universality of the concept, the 1-dimensional spring equations will be presented here. The term “spring” is interchangeable with “compressible layer” for the purposes of describing the presently disclosed technology. Substitution to a 3-D material can be made in the equations at any time using Young's modulus, the area and the thickness of the compressible layer [3].

$\begin{matrix} {F = {kx}} & \lbrack 1\rbrack \\ {F = {ma}} & \lbrack 2\rbrack \\ {k = \frac{YS}{L}} & \lbrack 3\rbrack \end{matrix}$

where k is the spring constant (N/m), x is the spring displacement from equilibrium, m is the mass of the body, a is the acceleration, Y is the Young's modulus (PA), S is the surface area (m²), and L is the thickness (m).

When a stress (force) is applied to a spring, the spring exhibits strain (displacement) according to Hooke's Law. Hooke's Law describes a proportional relationship between stress and strain. The maximum displacement of the spring x_(s-max) is constrained by the proportionality limit of the particular spring. The proportionality limit is the maximum amount of strain at which the material still satisfies Hooke's Law. The proportionality limit also applies to a solid used in a compressible layer. When a strain is greater than the proportionality limit, the material may continue to compress until the elastic limit is reached. The elastic limit for common compressible layer materials is the point at which the material will no longer compress under the normal range of forces from athletic activities. The proportionality limit may range as a percentage of total material thickness for different formulations. Although Hooke's Law does not strictly apply when the strain exceeds the proportionality limit, an increased stress is still required to create further strain. The maximum spring displacement x_(s-max) is here defined as the elastic limit.

One objective of running shoes is to provide shock attenuation (cushioning) of the forces imparted by the foot. Cushioning occurs when there is a change in kinetic energy over an interval of time and over a stopping distance. The stopping distance is equal to the amount of compression that occurs in the compressible structure. For a given change in kinetic energy, an average impact force can be defined as:

$\begin{matrix} {F_{{impact}\text{-}{avg}} = \frac{W_{net}}{d}} & \lbrack 4\rbrack \end{matrix}$

Where d is the stopping distance and W_(net) is the net work done by the change in kinetic energy and defined as:

W _(net)=½mv ² _(initial)−½mv ² _(final)  [5]

and v_(final) is equal to zero. The larger the stopping distance d, the longer the stopping time interval.

Cushioning is said to increase when the average impact force decreases. Equation 5 shows that an increasing stopping distance results in a lower average impact force. Therefore, cushioning is said to increase with a larger stopping distance and a longer stopping time interval.

Cushioning can also be understood as a negative acceleration (deceleration) of a mass in the context of Newton's second law F=ma. A lower deceleration, A lower deceleration equates to a lower average impact force and is also known as greater shock attenuation. Running shoes typically feature compressible layers with a range of thicknesses between 2 mm and 10 mm in the ball region, and 10 mm to 20 mm in the heel region, and a range of elastic stiffnesses. Together, the elastic properties and the thickness determine the effective spring constant. The negative accelerations can be analyzed assuming that the compressible layer behaves like a spring. Following Hooke's Law, the amount of cushioning (negative acceleration) achieved will depend on the force imparted and the spring constant of the compressible layer.

Another objective of running shoes is to limit the amount of energy loss during cushioning (compression of the spring) by returning energy to the runner. While this energy return is understood to be desirable, running shoe designs have not successfully achieved this goal. Energy return can occur in running shoes when the compressed spring releases its stored potential energy by expanding and providing a net upward force on the wearer's foot. The net upward force causes an acceleration and increasing kinetic energy. The total amount of potential energy (J) available for energy return can be computed from the spring constant and the length of compression:

PE=½kx ²  [6]

The length of compression can be calculated from Hooke's Law [1]. Thus, according to Eqn. 6, for a given spring constant, a longer length of compression will generate a higher potential energy. However, the maximum compression length, x, will be limited by the proportionality limit of the material. Thus, for any given shoe sole thickness and associated proportionality limit, there exists a maximum amount of energy available for conversion into kinetic energy in the runner (energy return).

Human running can be described as having a gait cycle which begins with the toe-off of the right foot, a flight period during which the left foot moves forward while both feet are in the air, a first contact period when the left foot is in contact with the ground until toe-off of the left foot, a second flight period during which the right foot moves forward while both feet are airborne, and a second contact period when the right foot is on the ground until the moment of toe-off. During each flight period, the center of mass for the body accelerates downward under the force of gravity an amount determined by the time period of the flight. The center of mass must, therefore, be accelerated back up during each contact period. A net upward force must act on the center of mass in order to produce the upward acceleration. According to Newton's Third Law, the net upward force will exhibit an equal and opposite downward force, called the ground reaction force. The runner's leg muscles generate the upward force. The ground reaction force can be measured over time with sensors placed under the runner's foot.

Slower running speeds are associated with longer ground contact times and lower peak ground reaction forces than faster running speeds. Conversely, faster running speeds are associated with shorter ground contact times and higher peak ground contact forces than slower running speeds. This can be understood from fundamental physics with the center of mass moving at a constant speed horizontally and for a specific cadence and flight period: A faster running speed allows less time for each foot to be in contact with the ground than a slower running speed. The shorter contact time means a shorter time to accelerate the center of mass upward for the beginning of the flight period. The shorter period requires a higher acceleration of the mass and a higher ground reaction force to generate it. Such contact times and ground reaction force magnitudes associated with different running speeds are readily observed in studies measuring these parameters [Hunter et al. 2014, Concejero 2013, Kram and Taylor 1990].

Ground reaction force data for barefoot runners using multi-nodal measurement systems (ex. Tekscan Inc. MatScan) show that the different parts of the foot (heel, ball-of-foot, and toes) each have unique and different force amplitudes and periods of impulse from each other. Multi-nodal measurement systems differ from a force plate measurement system in that they collect pressure data from a grid of many nodes [FIG. 1] compared to a single point using a rigid plate [FIG. 2]. Force plate systems measure an average of the force across the entire foot, but do not accurately measure the force at specific parts of the foot during the contact phase of the gait cycle. Multi-nodal systems have a typical spacing of 1-5 mm and a sampling frequency of 100 to 750 Hz. Multi-nodal force measurement allows the investigator to isolate and compare the force vs time sequences for different regions of the foot during the contact phase [FIG. 3] revealing the important force characteristics of each anatomical part of the foot. Such important force characteristics are unobservable using a force plate measurement system.

Using the multi-nodal system by ©Tekscan Inc. MatScan VersaTek™, the following observations were made.

First, the force amplitudes and force impulse frequencies differ for each region of the foot

[FIG. 4].

Second, the sum of the foot region force-time profiles produces the same force-time profile as a force plate measurement [FIG. 4].

Third, the forces during the contact phase include an impact force and a propulsion force and that these forces are present to different degrees in the different foot regions [FIG. 5]. The impulse frequency associated with the impact force is high relative the frequency of the propulsion impulse and this is consistent with the common understanding of impact forces from falling objects.

Fourth, the propulsion force magnitude and frequency increase with increasing runner speed for each foot region, but specifically for the ball region [FIG. 6]. This phenomenon can be explained as the higher propulsion force required to achieve the higher rate of vertical acceleration associated with faster running speeds. The force impulse generated from the muscle activation during propulsion is defined here to be F_(impulse). The relationship between peak force amplitude and runner speed is central to the presently disclosed technology.

Fifth, the force amplitudes and frequencies from each foot region are the same regardless of strike pattern [FIG. 7]. In other words, the measurements reveal that the force-time profiles for the heel, arch, ball, and toes, are the same whether the runner strikes first with the heel or first with the ball. This observation suggests that the ground reaction force characteristics are not driven by strike pattern.

These observations provide insights into the dynamic nature of the ground reaction forces during human running, walking, and jumping that were previously obscured. The insights alter the understanding of the kinematics and force dynamics involved in human ambulatory locomotion compared to the substantial body of previously published work in the field. Scientific studies and mathematical modeling based on force plate measurements support a theory of horizontal running where the ground reaction forces can be generally attributed to the masses of the runner's torso and legs segments and the force of gravity [Liu, Nigg 1999, Clark et al. 2017, Lieberman et al. 2010]. Modeling based on this theory produces force vs time profiles that closely match force plate measurements. However, the models, like the force plate measurement system, do not differentiate between different regions of the foot, nor can they explain peak force differences at different running speeds. The low spatial resolution of a force plate measurement system causes a simplification to the theory and mathematical models for running that doesn't include forces generated by a) leg muscles, or b) the mechanical role of the different regions of the foot. The simplified theories fail to identify the different timing, magnitude, and duration of the forces from the four anatomical regions of the foot, for runners of different masses, and for persons running at different speeds. Since shoe materials can only respond to forces directly adjacent to them, knowledge of how the forces vary by foot region is essential to engineering a compressible layer with specific performance attributes. The multi-nodal force measurements and the insights gleaned from them, allowed the development of a theory and mathematical model needed to engineer a compressible layer for optimal performance. The insights can be exploited to maximize the cushioning and storage of potential energy in running shoes by identifying the unique spring constant that maximizes the potential energy in the spring and satisfies the boundary conditions imposed by the shoe dimensions, material properties, runner speed, and runner mass. Specifically, knowledge of the different force magnitudes for different foot regions according to running speed zones, determines a specific set of boundary conditions. Applying the boundary conditions and the laws of physics creates a unique solution for the spring constant that maximizes the cushioning and potential energy available for energy return. Additionally, the physical dimensions of the compressible layer vary by foot region, creating different boundary conditions for each region.

The relevant boundary conditions include the compressible layer component thickness, the component's horizontal area, and the range of targeted body masses. Given a set of boundary conditions and a specified runner speed, a theoretical maximum potential energy, PE_(max), can be calculated. For a given set of boundary conditions, PE_(max) will vary as the specified runner speed is changed. A graph of the ratio of the actual potential energy generated, PE, at different actual running speeds, to PE_(max), illustrates how the amount of energy available for energy return to the runner drops off for ratios above and below 1.0 [FIG. 8a ]. For example, a shoe designed to maximize PE for a running speed of 3 m/s will provide less cushioning and energy return to the runner at speeds of 2 m/s or 4 m/s. The result can similarly be viewed in the graph depicting the ratio of potential energy to maximum potential energy for a runner at a fixed speed but with different values of the spring constant inherent in the shoe (i.e constant PE and varying PE_(max)) [FIG. 8 b].

A compressible layer will decompress (expand) back toward the original uncompressed dimension when the force is decreased and/or removed. In the case of a rapid removal of the force, the amount of reexpansion will depend on the makeup of the compressible layer. Materials used in compressible layers in footwear exhibit a range of reexpansion amounts relative to the original uncompressed dimension, which can be measured and expressed as a percentage. Typical reexpansion percentages range from 10% to 90% within the first tenths of a second after removal of the force. The percentage of reexpansion is related to the amount of stored potential energy that is actually converted to kinetic energy in the wearer and perceived as energy return.

Athletic footwear has been and continues to be manufactured for sports like running using compressible layers where the measured force magnitudes on the shoe at different running speeds are not considered during the design and engineering of the footwear and, consequently, the cushioning and energy return available to the athlete is a mere fraction of the potential maximum. Furthermore, athletic footwear does not explicitly consider different force elements and their associated impulse frequencies in the heel, arch, ball-of-foot, and toes, tending instead to treat the foot as a monolithic entity with respect to forces. The over-simplification of forces and shoe design eliminates the possibility of maximizing cushioning and energy return within the shoe regardless of runner speed, running form, or wearer's mass. The suboptimal results increase the strain on the wearer's body during the cushioning phase and increase the fatigue in the muscles and metabolic system during the energy return phase.

SUMMARY

By tuning the rebound properties of the compressible layer to a runner's speed and optionally to specific regions of the compressible layer, cushioning can be maximized and energy losses minimized. Cushioning is maximized when the compressible layer compresses to near its elastic limit under the forces of running. Energy losses are minimized when the vertical (downward) component of the wearer's kinetic energy is converted into potential energy in the compressible layer during compression, and at least some of that stored potential energy is subsequently returned to the wearer by generating vertical (upward) kinetic energy. The amount of stored potential energy is determined by the amount of compression and the maximum force applied. Energy storage is maximized when the compressible layer is compressed to near its elastic limit.

It will be appreciated that a faster running velocity necessitates a shorter ground contact time and higher associated ground reaction forces to generate the higher vertical acceleration of the body center of mass necessary to lift the body back up for the flight period between successive ground contact intervals (steps). A slower running velocity has longer contact times, requires a slower vertical acceleration of the center of mass, and is associated with lower peak ground reaction forces. The faster running speed will require that the compressible layer be tuned to the greater peak forces in order to store and return maximum energy to the runner's foot, while a slower running speed will require that the compressible layer be tuned to lesser forces. It will also be appreciated that any vertical kinetic energy not converted into stored potential energy will be lost and means that storing less spring potential energy will result in more energy loss.

It will further be appreciated that the mass of the runner will influence the forces necessary to achieve the vertical acceleration associated with a specific running speed. A higher mass will require a higher force to achieve the vertical acceleration. Within the normal range of human body mass for runners, the differences in ground reaction forces are primarily influenced by the required vertical acceleration, because kinetic energy changes with the square of the vertical velocity and is linearly proportional to the mass. Consequently, a given pair of running shoes embodying the presently disclosed technology will be tuned to a specific range of running speeds and a given range of body masses. Runners will choose their running shoes accordingly.

Different anatomical portions of the foot contact the ground at different times in the contact phase of the gait cycle, and also with different force magnitudes. Consequently, it may be beneficial to tune the portions of the midsole underlying distinct anatomical portions of the foot differently to take this into account. For example, the peak force in the heel is significantly lower than the peak force in the ball of foot region, requiring a lower spring constant in the heel than in the ball of foot in order to achieve similar amounts of compression. Similarly, the arch and toes regions experience lower peak forces relative to the ball and heel and require relatively lower spring constants.

It will also be appreciated that the amount of potential energy stored in the compressible layer increases with increasing compression of the compressible layer roughly according to Equation 6. Furthermore, the maximum potential energy is limited by the limit of elasticity, which is defined as the maximum compression, x_(s-max).

By means of the presently disclosed technology, a runner may recover a significant portion of the energy expended by the runner which would otherwise have been lost. Instead, the recovered energy will be used to provide a lift to the body as it accelerates upward. This returned energy will be small in each step but cumulatively will be a significant aid when running long distances.

An article of footwear is disclosed here as having an upper and a sole structure secured to the upper. The sole structure consists of one or more midsole components with an inherent spring constant such that the ratio of the midsole potential energy (PE) to the maximum midsole potential energy (PE_(max)), approaches a value of 1.0. The range in ratio represents a practical range of variance a runner's ability to control running speed, variation in body mass of +/−10 kg, manufacturing tolerances for typical midsole materials. The PE/PE_(max) ratio is computed using the vertical propulsion peak force magnitude, F_(impulse), associated with different running speeds and a given set of physical parameters that includes the midsole dimensions and a runner mass range. It is possible to determine the spring constant mathematically for each region of the midsole that will yield the greatest cushioning and potential energy available for energy return (the maximum potential energy) by measuring or calculating F_(impulse) for different running speeds from each adjacent point on the wearer's foot. In a preferred embodiment, the PE/PE_(max) ratio is between 0.95 and 1.05. In an alternative embodiment, the PE/PE_(max) ratio is between 0.85 and 1.15. In another alternative embodiment, the PE/PE_(max) ratio is between 0.80 and 1.20.

A midsole component can be tuned to a specific set of boundary conditions at a point on the midsole, an area of the midsole, or at multiple different areas of the midsole. By treating the midsole as having four regions in the transverse plane that correspond to the heel, arch, ball-of-foot, and toes of the wearer's foot, the midsole can be constructed with separately tuned regions

In one embodiment of the presently disclosed technology, the midsole is constructed with four regions corresponding anatomically to the wearer's heel, arch, ball-of-foot, and toes, each region being comprised entirely of, or encompassing within it, a tuned midsole structure. Furthermore, the preferred embodiment will have midsole structures that are tuned according to the wearer running speed and wearer mass.

In an alternate embodiment of the presently disclosed technology, the four anatomical midsole regions can be further divided into subregions. The subregions may be of any shape or size that fit within the anatomically defined region. In one embodiment, the subregions are squares with dimensions of 4 mm×4 mm. Each subregion can be tuned to the specific forces acting on it by the corresponding anatomical subregion of the wearer's foot.

By rearranging the terms algebraically, the PE/PE_(max) ratio can be expressed as a ratio of the actual spring constant, k, to an ideal spring constant, k_(ideal). The k/k_(ideal) ratio can practically be applied to the manufacture of midsole components.

Midsole structures are comprised of one or more materials and assembled in such a way as to exhibit spring-like properties according to Hooke's Law when acted on by a compressive force. The effect may be achieved in a multitude of ways using materials and constructions common in the industry and with physical dimensions and masses suitable for performance athletic footwear. A practical engineering approach to determine the midsole component physical properties is to apply the relevant F_(impulse) for the runner mass and speed, the elastic limit for the compressible component, and Hooke's Law, to calculate the spring constant, k_(ideal), that equates to the maximum spring displacement x_(s-max). Physical properties for an elastic solid can by derived from the spring constant and the conversion for Young's modulus.

$\begin{matrix} {Y = \frac{k_{ideal}L}{S}} & \lbrack 5\rbrack \end{matrix}$

where Y is the Young's modulus, L is the depth of the material, and S is the surface area of the material.

Springs and elastic solids exhibit varying degrees of energy loss (damping) during a rebound cycle. The amount of energy loss will constrain the efficiency with which the spring element can convert its stored potential energy into kinetic energy. However, a high damping coefficient, and therefore a high energy loss, does not change the applicability of Hooke's Law to spring displacements below the proportionality limit. It is understood that the higher the percentage of decompression in the compressible layer, the greater the amount of the stored potential energy that is returned to the wearer.

In one embodiment of the presently disclosed technology, any compressible component(s) incorporated into the shoe design will decompress (reexpand) to a high percentage of the original uncompressed dimension, reexpanding 90%. In an alternate embodiment, any of the compressible component swill decompress to a lesser percentage of 50%. In a further alternate embodiment, any of the compressible components we decompress to low percentage of 25%. In all embodiments, the compressible components within a single shoe may decompress by different percentages from each other.

A running shoe consisting of (a) an upper that secures the foot to the shoe, and (b) a compressible sole structure under the upper that compresses in proportion to the amount of pressure applied during the gait cycle of the runner to no more than the limit of elasticity and decompresses when pressure is decreased and removed from the compressible sole structure during the ground contact phase of the gait cycle of the runner, can be constructed so that it is tuned to a runner's running speed as follows.

This is done by taking into account the runner's gait cycle. The gait cycle of the runner to which the shoe is tuned consists of: first, a time when the shoe initially contacts the ground; second, a time during which gravity and the runner's leg muscles apply increasing force to the shoe; third, a time of maximum application of force to the shoe, fourth, a time of application of decreasing force to the shoe until the force applied to the shoe is zero but the shoe remains in contact with the ground; fifth, a time when the shoe is removed from contact with the ground; sixth, a time when the shoe is moved forward before again contacting the ground.

The compressible sole layer is constructed so that it compresses to no more than its limit of elasticity upon application of increasing force to the shoe during the initial stage of the stride, and decompresses in response to decreasing force during the time after the maximum application of force to the shoe and until the shoe leaves the ground. The compressible sole layer most preferably decompresses substantially completely during the time after the maximum application of force to the shoe during the contact period of the runner and before the shoe leaves the ground during the gait cycle of the runner, but may decompress only 90% or even only 50%. In one embodiment, the compressible sole layer consists of a plurality of regions, each region of the compressible sole layer below a corresponding region of the foot (e.g. the heel, ball, and toe regions) and tuned to the forces applied to that region of the compressible sole layer by the corresponding region of the foot. The shoe can be tuned so that the cushioning and energy return are maximized for a running speed zone by tuning the ratio of k/k_(ideal) to approach a value of 1.0. A shoe according to this technology is tuned to match a runner's speed, preferably +/−0.3 m/s, but may also be tuned to match the runner's speed +/−1 m/s, or even +/−2 m/s.

The advantages and features of novelty characterizing aspects of the presently disclosed technology are pointed out with particularity in the appended claims. To gain an improved understanding of the advantages and features of novelty, however, reference may be made to the following descriptive matter and accompanying figures that describe and illustrate various configurations and concepts related to the presently disclosed technology.

BRIEF DESCRIPTION OF THE DRAWINGS

The presently disclosed technology will be better understood in light of the accompanying figures.

FIG. 1 depicts an array of pressure measuring nodes arranged in an orthogonal matrix with spacing of 5.8 mm.

FIG. 2 is a schematic for a typical force plate used in biomechanical studies.

FIG. 3 is a plot of peak vertical ground reaction force from the plantar foot surface of a human runner with the anatomical regions (heel, arch, ball, toes) demarcated with boxes.

FIG. 4 is a graph depicting the vertical ground reaction force vs time profiles of four anatomical regions (heel, arch, ball, toes) of the foot for a single step of a runner overlaid on the profile for the sum of all forces vs time.

FIG. 5 is an annotated graph depicting vertical ground reaction forces vs time profiles from a human runner with callouts marking the impact forces and the propulsion forces.

FIG. 6 is a graph of vertical ground reaction force vs time profiles from the ball-of-foot region of a runner for a series of steps with progressively increasing runner speed.

FIG. 7 is an annotated graph depicting vertical ground reaction forces vs time profiles from four regions of the foot experiencing a forefoot-strike pattern.

FIGS. 8a and 8b are graphs of PE/PE_(max) vs runner speed and midsole spring constant respectively.

FIG. 9 is lateral side elevational view of an article of footwear.

FIG. 10 is a medial side elevational view of the article of footwear.

FIG. 11 is an exploded perspective view of a sole structure of the article of footwear.

FIGS. 12a and 12b are cross-sectional views of the sole structure, as defined by lateral and longitudinal section lines 4A and 4B in FIG. 11.

FIGS. 13a and 13b are cross-sectional views of the sole structure, as defined by section lines 4A and 4B in FIG. 11.

DETAILED DESCRIPTION

The following discussion and accompanying figures disclose various sole structure configurations for articles of footwear. Concepts related to the sole structure configurations are disclosed with reference to footwear that is suitable for running. The sole structure configurations are not limited to footwear designed for running, however, and may be utilized with a wide range of athletic footwear styles, including basketball shoes, cross-training shoes, cycling shoes, football shoes, soccer shoes, tennis shoes, and walking shoes, for example. The sole structure configurations may also be utilized with footwear styles that are generally considered to be non-athletic, including dress shoes, loafers, sandals, and boots. The concepts disclosed herein may, therefore, apply to a wide variety of footwear styles, in addition to the specific style discussed in the following material and depicted in the accompanying figures.

General Footwear Structure

An article of footwear 10 is depicted in FIGS. 9 and 10 as including an upper 20 and a sole structure 30. For reference purposes, footwear 10 may be divided into four general regions: a toes region 11, a ball-of-foot region 12, a midfoot region 13, and a heel region 14, as shown in FIGS. 9 and 10. Footwear 10 also includes a lateral side 15 and a medial side 16. Toes region 11 generally includes portions of footwear 10 corresponding with the phalanges. Ball-of-foot region 12 generally includes portions of footwear 10 corresponding with the joints between the metatarsals and the phalanges and the metatarsal bones, midfoot region 13 generally includes portions of the arch (both medial and lateral arches) in an area below the tarsal bones, and heel region 14 corresponds with the rear portion of the foot, including the calcaneus bone. Lateral side 15 and medial side 16 extend through each of regions 11-14 and correspond with opposite sides of footwear 10. Regions 11-14 and sides 15-16 are not intended to demarcate precise areas of footwear 10. Rather, regions 11-14 and sides 15-16 are intended to represent general areas of footwear 10 to aid in the following discussion. In addition to footwear 10, regions 11-14 and sides 15-16 may also be applied to upper 20, sole structure 30, and individual elements thereof.

Upper 20 is depicted as having a substantially conventional configuration incorporating a plurality material elements (e.g., textiles, foam, leather, and synthetic leather) that are stitched or adhesively bonded together to form an interior void for securely and comfortably receiving a foot. The material elements may be selected and located with respect to upper 20 in order to selectively impart properties of durability, air-permeability, wear-resistance, flexibility, and comfort, for example. An ankle opening 21 in heel region 14 provides access to the interior void. In addition, upper 20 may include a lace 22 that is utilized in a conventional manner to modify the dimensions of the interior void, thereby securing the foot within the interior void and facilitating entry and removal of the foot from the interior void. Lace 22 may extend through apertures in upper 20, and a tongue portion of upper 20 may extend between the interior void and lace 22. Given that various aspects of the present discussion primarily relate to sole structure 30, upper 20 may exhibit the general configuration discussed above or the general configuration of practically any other conventional or non-conventional upper. Other devices, such as Velcro tabs, can be substituted for laces. Accordingly, the structure of upper 20 may vary significantly within the scope of the presently disclosed technology.

Sole structure 30 is secured to upper 20 and has a configuration that extends between upper 20 and the ground. In general, the various elements of sole structure 30 exhibit rebound properties (impart cushioning and energy return), affect the overall motion of the foot, and impart traction during walking, running, or other ambulatory activities. Additional details concerning the configuration of sole structure 30 will be described below.

General Sole Structure Configuration

Sole structure 30 is depicted in FIG. 11 and includes a midsole element 40 and an outsole 50. In addition to these elements, sole structure 30 may incorporate one or more plates, moderators, or spring-like structures, for example, which further enhance the ground reaction force cushioning and potential energy storage characteristics of sole structure 30 or the performance properties of footwear 10. Additionally, sole structure 30 may incorporate a sockliner (not depicted) that is located within a lower portion of the void in upper 20 to enhance the comfort of footwear 10.

Midsole element 40 extends throughout a length of footwear 10 (i.e., through each of regions 11-14) and a width of footwear 10 (i.e., between sides 15 and 16). The primary surfaces of midsole element 40 are an upper surface 41, an opposite lower surface 42, and a side surface 43 that extends between surfaces 41 and 42. Upper surface 41 is joined to a lower area of upper 20, thereby joining sole structure 30 to upper 20. Lower surface 42 is joined with outsole 50 in regions 11-14. Surface 42 may also serve as outsole 50 in portions of regions 11-14, none of surface 42 or the entirety of surface 42. Additionally, side surface 43 forms an exposed sidewall of sole structure 30 on both lateral side 15 and medial side 16.

A variety of materials may be utilized to form midsole element 40. As an example, midsole element 40 may be formed from a polymer foam material, such as polyurethane or ethylvinylacetate and exhibit the functional properties of rebound according to desired design specifications. In some configurations, midsole element 40 may also be (a) a plate formed from a semi-rigid polymer material or (b) a combination of a plate and foam material, (c) a plurality of foam-based and semi-rigid structures. In addition to the foam material, midsole element 40 may incorporate one or more foam elements defined spatially and with modulus Y, semi-rigid structures with spatial dimensions S and L and net modulus Y, for example, that create the rebound characteristics of sole structure 30 or the overall performance properties of footwear 10. In some configurations, midsole element 40 may also encapsulate foam-based, semi-rigid, and combination structures within a foam chassis 41. In other configurations, midsole element 40 may encapsulate foam-based, semi-rigid, and combination structures within a portion of regions 11-14. Midsole element 40 may also comprise no encapsulating materials, allowing the foam-based, semi-rigid, and combination structures to be exposed along the sidewall 43 and bonded directly to upper 20 and to outsole 50, where an outsole 50 is present.

The midsole can be divided into several regions along the length of the shoe as shown in FIGS. 9 & 12. Individual midsole structural elements 60 encapsulated within a foam chassis 41 may be configured as in FIGS. 12a and 12 b. Midsole elements 60 may be formed of a wide range of polymer materials with engineering properties of the materials (e.g., tensile strength, stretch properties, fatigue characteristics, dynamic modulus, and loss tangent) as well as the ability of the materials to prevent the diffusion of any fluid contained within chamber walls. The sum behavior of all the materials comprising a single region (11, 12, 13, or 14) located directly under the corresponding foot anatomical feature will generate the net rebound effect in the specified region of the midsole. The particular placement, shape, and size of individual elements 60 may vary greatly between embodiments. The number of elements 60 and the arrangement of the elements within the chassis 41 as shown in FIGS. 12a and 12 b, represent a single example and does not represent the possible variety of configurations available to the designers within the context of the presently disclosed technology.

Midsole element 40 may be comprised entirely of structural elements 60 with no encapsulating foam element 41, as depicted in FIGS. 13a and 13 b. Midsole 40 may include voids of open space 61, and may expose any of the outer surfaces or may cover those surfaces with paint, film, cloth, or other polymer material 62 for the purposes of abrasion resistance or cosmetics. Outer surface coatings 62 may or may not contribute to the rebound characteristics of the structural elements 60 and the midsole element 40.

The presently disclosed technology is disclosed above and in the accompanying figures with reference to a variety of configurations. The purpose served by the disclosure, however, is to provide an example of the various features and concepts related to the invention, not to limit the scope of the invention. One skilled in the relevant art will recognize that numerous variations and modifications may be made to the configurations described above without departing from the scope of the present invention, as defined by the appended claims. 

1.-18. (canceled)
 19. A running shoe tuned to a running speed of a runner wearing the shoe, the shoe consisting of (a) an upper that secures the foot to the shoe, and (b) a compressible sole structure under the upper that compresses in proportion to the amount of pressure applied during the gait cycle of the runner to no more than the limit of elasticity and decompresses when pressure is decreased and removed from the compressible sole structure during the ground contact phase of the gait cycle of the runner, the shoe characterized in that: i) the gait cycle of the runner to which the shoe is tuned consists of: first, a time when the shoe initially contacts the ground; second, a time during which gravity and the runner's leg muscles apply increasing force to the shoe; third, a time of maximum application of force to the shoe, fourth, a time of application of decreasing force to the shoe until the force applied to the shoe is zero but the shoe remains in contact with the ground; fifth, a time when the shoe is removed from contact with the ground; sixth, a time when the shoe is moved forward before again contacting the ground, ii) the compressible sole layer compresses to no more than its limit of elasticity upon application of increasing force to the shoe during the initial stage of the stride, iii) the compressible sole layer decompresses in response to decreasing force during the time after the maximum application of force to the shoe and until the shoe leaves the ground.
 20. The running shoe of claim 19, wherein the compressible sole layer decompresses substantially completely during the time after the maximum application of force to the shoe during the contact period of the runner and before the shoe leaves the ground during the gait cycle of the runner.
 21. The running shoe of claim 19, wherein the compressible sole layer decompresses at least 90% during the time from after the maximum application of force to the shoe during the contact period of the runner and before the shoe leaves the ground during the gait cycle of the runner.
 22. The running shoe of claim 19, wherein the compressible sole layer decompresses at least 50% during the time from after the maximum application of force to the shoe during the contact period of the runner and before the shoe leaves the ground during the gait cycle of the runner.
 23. The running shoe of claim 19, wherein the compressible sole layer consists of a plurality of regions, each region of the compressible sole layer below a corresponding region of the foot and tuned to the forces applied to that region of the compressible sole layer by the corresponding region of the foot.
 24. The running shoe of claim 23, wherein each of the plurality of regions of the compressible sole layer decompresses substantially completely during the time after the maximum application of force to that region of the compressible sole layer during the contact period of the runner and before the corresponding portion of the outer sole leaves the ground during the gait cycle of the runner.
 25. The running shoe of claim 23, wherein each of the plurality of regions of the compressible sole layer decompresses at least 90% during the time from the maximum application of force to that region of the compressible sole to the time when the shoe leaves the ground.
 26. The running shoe of claim 23, wherein each of the plurality of regions of the compressible sole layer decompresses at least 50% during the time from the maximum application of force to that region of the compressible sole to the time when the shoe leaves the ground.
 27. The running shoe of claim 23, wherein the regions of the foot consist of (a) the heel of the runner's foot, (b) the ball of the runner's foot, (c) the arch of the runner's foot, (d) the toes of the runner's foot.
 28. The running shoe of claim 23, wherein the regions of the foot consist of any subregion of the plantar surface of the runner's foot that may exert a differential force onto an adjacent subregion of the compressible layer.
 29. An article of footwear having an upper and a compressible structure secured to the upper, the compressible structure providing cushioning and energy return to the wearer by means of first compression of the compressible structure followed by expansion of the compressible structure.
 30. The article of footwear as in claim 29, wherein the cushioning and energy return are maximized for a running speed zone by tuning the ratio of k/k_(ideal) to approach a value of 1.0.
 31. The article of footwear as in claim 29, wherein the compressible structures are tuned to a progression of runner speeds and allow for distinct versions of the footwear differentiated by runner speed zone.
 32. The article of footwear as in claim 31, wherein the runner is matched to a particular footwear version according to the runner's intended running speed.
 33. The article of footwear as in claim 31, wherein the runner's intended running speed has a midpoint speed and a range of +/−0.3 m/s.
 34. The article of footwear as in claim 31, wherein the runner's intended running speed has a midpoint speed and a range of +/−1 m/s.
 35. The article of footwear as in claim 31, wherein the runner's intended running speed has a midpoint speed and a range of +/−2 m/s.
 36. The running shoe of claim 19, further comprising a midsole element formed from polyurethane or ethylvinylacetate.
 37. The article of footwear as in claim 31, further comprising a midsole element including at least one of (a) a plate formed from a semi-rigid polymer material, (b) a combination of a plate and foam material, or (c) a plurality of foam-based and semi-rigid structures. 